TSTP Solution File: NUM542+2 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM542+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 10:44:55 EDT 2023
% Result : Theorem 10.53s 11.03s
% Output : Proof 10.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM542+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.15 % Command : do_cvc5 %s %d
% 0.19/0.36 % Computer : n026.cluster.edu
% 0.19/0.36 % Model : x86_64 x86_64
% 0.19/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.36 % Memory : 8042.1875MB
% 0.19/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.36 % CPULimit : 300
% 0.19/0.36 % WCLimit : 300
% 0.19/0.36 % DateTime : Fri Aug 25 16:23:48 EDT 2023
% 0.19/0.36 % CPUTime :
% 0.22/0.50 %----Proving TF0_NAR, FOF, or CNF
% 10.53/11.03 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.3Tky8ohPxA/cvc5---1.0.5_28182.p...
% 10.53/11.03 ------- get file name : TPTP file name is NUM542+2
% 10.53/11.03 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_28182.smt2...
% 10.53/11.03 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 10.53/11.03 --- Run --no-e-matching --full-saturate-quant at 5...
% 10.53/11.03 % SZS status Theorem for NUM542+2
% 10.53/11.03 % SZS output start Proof for NUM542+2
% 10.53/11.03 (
% 10.53/11.03 (let ((_let_1 (tptp.sdtlseqdt0 tptp.xm tptp.xn))) (let ((_let_2 (tptp.slbdtrb0 tptp.xn))) (let ((_let_3 (tptp.slbdtrb0 tptp.xm))) (let ((_let_4 (tptp.aSubsetOf0 _let_3 _let_2))) (let ((_let_5 (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 (tptp.slbdtrb0 tptp.xn)) (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 W0) tptp.xn)))))) (let ((_let_6 (tptp.aSet0 _let_2))) (let ((_let_7 (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 (tptp.slbdtrb0 tptp.xm)) (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 W0) tptp.xm)))))) (let ((_let_8 (tptp.aSet0 _let_3))) (let ((_let_9 (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 (tptp.slbdtrb0 tptp.xn)) (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 W0) tptp.xn)))))) (let ((_let_10 (and _let_6 _let_9))) (let ((_let_11 (forall ((W0 $$unsorted)) (= (tptp.aElementOf0 W0 (tptp.slbdtrb0 tptp.xm)) (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 W0) tptp.xm)))))) (let ((_let_12 (and _let_8 _let_11))) (let ((_let_13 (not (and (=> _let_1 (=> _let_12 (=> _let_10 (or (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 (tptp.slbdtrb0 tptp.xm)) (tptp.aElementOf0 W0 (tptp.slbdtrb0 tptp.xn)))) _let_4)))) (=> (and _let_8 _let_7 _let_6 _let_5 (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 (tptp.slbdtrb0 tptp.xm)) (tptp.aElementOf0 W0 (tptp.slbdtrb0 tptp.xn)))) _let_4) _let_1))))) (let ((_let_14 (tptp.aElementOf0 tptp.xn tptp.szNzAzT0))) (let ((_let_15 (tptp.aElementOf0 tptp.xm tptp.szNzAzT0))) (let ((_let_16 (and _let_15 _let_14))) (let ((_let_17 (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (forall ((W1 $$unsorted)) (= (= W1 (tptp.slbdtrb0 W0)) (and (tptp.aSet0 W1) (forall ((W2 $$unsorted)) (= (tptp.aElementOf0 W2 W1) (and (tptp.aElementOf0 W2 tptp.szNzAzT0) (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 W2) W0))))))))))) (let ((_let_18 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (or (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 W1) W0)))))) (let ((_let_19 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0) (tptp.aElementOf0 W2 tptp.szNzAzT0)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W2)) (tptp.sdtlseqdt0 W0 W2)))))) (let ((_let_20 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W0)) (= W0 W1)))))) (let ((_let_21 (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.sdtlseqdt0 W0 (tptp.szszuzczcdt0 W0)))))) (let ((_let_22 (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (not (= W0 (tptp.szszuzczcdt0 W0))))))) (let ((_let_23 (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.szszuzczcdt0 W0))) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (and (tptp.aElementOf0 _let_1 tptp.szNzAzT0) (not (= _let_1 tptp.sz00)))))))) (let ((_let_24 (forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 (tptp.slbdtrb0 tptp.xm))) (tptp.aElementOf0 W0 (tptp.slbdtrb0 tptp.xn)))))) (let ((_let_25 (tptp.aElementOf0 tptp.xn _let_2))) (let ((_let_26 (tptp.aElementOf0 tptp.xn _let_3))) (let ((_let_27 (not _let_26))) (let ((_let_28 (or _let_27 _let_25))) (let ((_let_29 (forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 (tptp.slbdtrb0 tptp.xm))) (tptp.aElementOf0 W0 (tptp.slbdtrb0 tptp.xn)))))) (let ((_let_30 (and _let_8 _let_7 _let_6 _let_5 _let_29 _let_4))) (let ((_let_31 (=> _let_30 _let_1))) (let ((_let_32 (or _let_24 _let_4))) (let ((_let_33 (=> _let_10 _let_32))) (let ((_let_34 (=> _let_12 _let_33))) (let ((_let_35 (=> _let_1 _let_34))) (let ((_let_36 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_2))) (let ((_let_37 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_3))) (let ((_let_38 (not _let_37))) (let ((_let_39 (or _let_38 _let_36))) (let ((_let_40 (tptp.szszuzczcdt0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_41 (tptp.sdtlseqdt0 _let_40 tptp.xm))) (let ((_let_42 (tptp.aElementOf0 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.szNzAzT0))) (let ((_let_43 (and _let_42 _let_41))) (let ((_let_44 (= _let_37 _let_43))) (let ((_let_45 (tptp.sdtlseqdt0 _let_40 tptp.xn))) (let ((_let_46 (and _let_42 _let_45))) (let ((_let_47 (= _let_36 _let_46))) (let ((_let_48 (tptp.aElementOf0 _let_40 tptp.szNzAzT0))) (let ((_let_49 (and _let_48 (not (= tptp.sz00 _let_40))))) (let ((_let_50 (not _let_42))) (let ((_let_51 (or _let_50 _let_49))) (let ((_let_52 (not _let_1))) (let ((_let_53 (not _let_41))) (let ((_let_54 (not _let_14))) (let ((_let_55 (not _let_15))) (let ((_let_56 (not _let_48))) (let ((_let_57 (or _let_56 _let_55 _let_54 _let_53 _let_52 _let_45))) (let ((_let_58 (_let_31))) (let ((_let_59 (NOT_AND (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_60 (_let_35))) (let ((_let_61 (or))) (let ((_let_62 (not _let_24))) (let ((_let_63 (_let_62))) (let ((_let_64 (forall ((W2 $$unsorted)) (= (and (tptp.aElementOf0 W2 tptp.szNzAzT0) (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 W2) tptp.xm)) (tptp.aElementOf0 W2 (tptp.slbdtrb0 tptp.xm)))))) (let ((_let_65 (and _let_8 _let_64))) (let ((_let_66 (or _let_55 _let_65))) (let ((_let_67 (forall ((W0 $$unsorted) (BOUND_VARIABLE_1976 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.szNzAzT0)) (= (= (tptp.slbdtrb0 W0) BOUND_VARIABLE_1976) (and (tptp.aSet0 BOUND_VARIABLE_1976) (forall ((W2 $$unsorted)) (= (and (tptp.aElementOf0 W2 tptp.szNzAzT0) (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 W2) W0)) (tptp.aElementOf0 W2 BOUND_VARIABLE_1976))))))))) (let ((_let_68 (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_69 (_let_67))) (let ((_let_70 (ASSUME :args (_let_16)))) (let ((_let_71 (AND_ELIM _let_70 :args (0)))) (let ((_let_72 (MACRO_RESOLUTION_TRUST (EQUIV_ELIM2 (TRANS (ALPHA_EQUIV :args (_let_11 (= W0 W2))) (MACRO_SR_PRED_INTRO :args ((= (forall ((W2 $$unsorted)) (= (tptp.aElementOf0 W2 (tptp.slbdtrb0 tptp.xm)) (and (tptp.aElementOf0 W2 tptp.szNzAzT0) (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 W2) tptp.xm)))) _let_64) SB_DEFAULT SBA_SEQUENTIAL RW_EXT_REWRITE)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_65 1)) :args ((or _let_64 (not _let_65)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_66)) :args ((or _let_55 _let_65 (not _let_66)))) _let_71 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_68 :args (tptp.xm _let_3 QUANTIFIERS_INST_CBQI_PROP)) :args _let_69))) _let_68 :args (_let_66 false _let_67)) :args (_let_65 false _let_15 false _let_66)) :args (_let_64 false _let_65)) :args (_let_11 false _let_64)))) (let ((_let_73 (_let_11))) (let ((_let_74 (ASSUME :args _let_73))) (let ((_let_75 (forall ((W2 $$unsorted)) (= (and (tptp.aElementOf0 W2 tptp.szNzAzT0) (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 W2) tptp.xn)) (tptp.aElementOf0 W2 (tptp.slbdtrb0 tptp.xn)))))) (let ((_let_76 (and _let_6 _let_75))) (let ((_let_77 (or _let_54 _let_76))) (let ((_let_78 (AND_ELIM _let_70 :args (1)))) (let ((_let_79 (MACRO_RESOLUTION_TRUST (EQUIV_ELIM2 (TRANS (ALPHA_EQUIV :args (_let_9 (= W0 W2))) (MACRO_SR_PRED_INTRO :args ((= (forall ((W2 $$unsorted)) (= (tptp.aElementOf0 W2 (tptp.slbdtrb0 tptp.xn)) (and (tptp.aElementOf0 W2 tptp.szNzAzT0) (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 W2) tptp.xn)))) _let_75) SB_DEFAULT SBA_SEQUENTIAL RW_EXT_REWRITE)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_76 1)) :args ((or _let_75 (not _let_76)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_77)) :args ((or _let_54 _let_76 (not _let_77)))) _let_78 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_68 :args (tptp.xn _let_2 QUANTIFIERS_INST_CBQI_PROP)) :args _let_69))) _let_68 :args (_let_77 false _let_67)) :args (_let_76 false _let_14 false _let_77)) :args (_let_75 false _let_76)) :args (_let_9 false _let_75)))) (let ((_let_80 (_let_9))) (let ((_let_81 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_ENUM))) (let ((_let_82 (ASSUME :args _let_80))) (let ((_let_83 (not _let_43))) (let ((_let_84 (forall ((W0 $$unsorted)) (let ((_let_1 (tptp.szszuzczcdt0 W0))) (or (not (tptp.aElementOf0 W0 tptp.szNzAzT0)) (and (tptp.aElementOf0 _let_1 tptp.szNzAzT0) (not (= tptp.sz00 _let_1)))))))) (let ((_let_85 (EQ_RESOLVE (ASSUME :args (_let_23)) (MACRO_SR_EQ_INTRO :args (_let_23 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_86 (_let_84))) (let ((_let_87 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.szNzAzT0)) (not (tptp.aElementOf0 W1 tptp.szNzAzT0)) (not (tptp.aElementOf0 W2 tptp.szNzAzT0)) (not (tptp.sdtlseqdt0 W0 W1)) (not (tptp.sdtlseqdt0 W1 W2)) (tptp.sdtlseqdt0 W0 W2))))) (let ((_let_88 (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO :args (_let_19 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_89 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_49 0)) :args ((or _let_48 (not _let_49)))) (REORDERING (CNF_OR_POS :args (_let_57)) :args ((or _let_55 _let_54 _let_52 _let_53 _let_45 _let_56 (not _let_57)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_88 :args (_let_40 tptp.xm tptp.xn QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_87))) _let_88 :args (_let_57 false _let_87)) _let_78 _let_71 (REORDERING (CNF_OR_POS :args (_let_51)) :args ((or _let_50 _let_49 (not _let_51)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_85 :args _let_81) :args _let_86)) _let_85 :args (_let_51 false _let_84)) (REORDERING (CNF_AND_NEG :args (_let_46)) :args ((or _let_50 _let_46 (not _let_45)))) (REORDERING (CNF_AND_POS :args (_let_43 1)) :args ((or _let_41 _let_83))) (REORDERING (CNF_AND_POS :args (_let_43 0)) :args ((or _let_42 _let_83))) (REORDERING (CNF_EQUIV_POS2 :args (_let_47)) :args ((or _let_36 (not _let_46) (not _let_47)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_82 :args _let_81) :args _let_80)) _let_79 :args (_let_47 false _let_9)) (REORDERING (CNF_EQUIV_POS1 :args (_let_44)) :args ((or _let_38 _let_43 (not _let_44)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_74 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_73)) _let_72 :args (_let_44 false _let_11)) (CNF_OR_NEG :args (_let_39 1)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_39 0)) (CONG (REFL :args (_let_39)) (MACRO_SR_PRED_INTRO :args ((= (not _let_38) _let_37))) :args _let_61)) :args ((or _let_37 _let_39))) (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_63)) :args _let_63)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_62) _let_24))) (REFL :args ((not _let_39))) :args _let_61)) (CNF_OR_NEG :args (_let_32 0)) (CNF_IMPLIES_NEG2 :args (_let_33)) (CNF_IMPLIES_NEG2 :args (_let_34)) (CNF_IMPLIES_NEG2 :args _let_60) _let_59 (CNF_IMPLIES_NEG2 :args _let_58) :args (_let_52 true _let_48 false _let_57 false _let_14 false _let_15 false _let_49 false _let_51 true _let_45 false _let_41 false _let_42 true _let_46 false _let_47 false _let_43 false _let_44 true _let_36 false _let_37 true _let_39 true _let_24 true _let_32 true _let_33 true _let_34 true _let_35 false _let_31)))) (let ((_let_90 (not _let_28))) (let ((_let_91 (tptp.szszuzczcdt0 tptp.xn))) (let ((_let_92 (tptp.sdtlseqdt0 _let_91 tptp.xm))) (let ((_let_93 (and _let_14 _let_92))) (let ((_let_94 (= _let_26 _let_93))) (let ((_let_95 (tptp.xn QUANTIFIERS_INST_ENUM))) (let ((_let_96 (or _let_55 _let_54 _let_1 _let_92))) (let ((_let_97 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.szNzAzT0)) (not (tptp.aElementOf0 W1 tptp.szNzAzT0)) (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 W1) W0))))) (let ((_let_98 (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_99 (tptp.sdtlseqdt0 _let_91 tptp.xn))) (let ((_let_100 (and _let_14 _let_99))) (let ((_let_101 (= _let_25 _let_100))) (let ((_let_102 (not _let_25))) (let ((_let_103 (not _let_100))) (let ((_let_104 (= tptp.xn _let_91))) (let ((_let_105 (not _let_99))) (let ((_let_106 (tptp.sdtlseqdt0 tptp.xn _let_91))) (let ((_let_107 (not _let_106))) (let ((_let_108 (tptp.aElementOf0 _let_91 tptp.szNzAzT0))) (let ((_let_109 (not _let_108))) (let ((_let_110 (or _let_54 _let_109 _let_107 _let_105 _let_104))) (let ((_let_111 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.szNzAzT0)) (not (tptp.aElementOf0 W1 tptp.szNzAzT0)) (not (tptp.sdtlseqdt0 W0 W1)) (not (tptp.sdtlseqdt0 W1 W0)) (= W0 W1))))) (let ((_let_112 (EQ_RESOLVE (ASSUME :args (_let_20)) (MACRO_SR_EQ_INTRO :args (_let_20 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_113 (or _let_54 _let_106))) (let ((_let_114 (forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.szNzAzT0)) (tptp.sdtlseqdt0 W0 (tptp.szszuzczcdt0 W0)))))) (let ((_let_115 (EQ_RESOLVE (ASSUME :args (_let_21)) (MACRO_SR_EQ_INTRO :args (_let_21 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_116 (and _let_108 (not (= tptp.sz00 _let_91))))) (let ((_let_117 (or _let_54 _let_116))) (let ((_let_118 (not _let_104))) (let ((_let_119 (or _let_54 _let_118))) (let ((_let_120 (forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.szNzAzT0)) (not (= W0 (tptp.szszuzczcdt0 W0))))))) (let ((_let_121 (EQ_RESOLVE (ASSUME :args (_let_22)) (MACRO_SR_EQ_INTRO :args (_let_22 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_122 (_let_24))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_122) :args (tptp.xn QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_122)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_28)) :args ((or _let_25 _let_27 _let_90))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_101)) :args ((or _let_100 _let_102 (not _let_101)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_100 1)) :args ((or _let_99 _let_103))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_110)) :args ((or _let_54 _let_104 _let_109 _let_107 _let_105 (not _let_110)))) _let_78 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_119)) :args ((or _let_54 _let_118 (not _let_119)))) _let_78 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_121 :args _let_95) :args (_let_120))) _let_121 :args (_let_119 false _let_120)) :args (_let_118 false _let_14 false _let_119)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_116 0)) :args ((or _let_108 (not _let_116)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_117)) :args ((or _let_54 _let_116 (not _let_117)))) _let_78 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_85 :args _let_95) :args _let_86)) _let_85 :args (_let_117 false _let_84)) :args (_let_116 false _let_14 false _let_117)) :args (_let_108 false _let_116)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_113)) :args ((or _let_54 _let_106 (not _let_113)))) _let_78 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_115 :args _let_95) :args (_let_114))) _let_115 :args (_let_113 false _let_114)) :args (_let_106 false _let_14 false _let_113)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_112 :args (tptp.xn _let_91 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_111))) _let_112 :args (_let_110 false _let_111)) :args (_let_105 false _let_14 true _let_104 false _let_108 false _let_106 false _let_110)) :args (_let_103 true _let_99)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_82 :args _let_95) :args _let_80)) _let_79 :args (_let_101 false _let_9)) :args (_let_102 true _let_100 false _let_101)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_94)) :args ((or _let_26 (not _let_93) (not _let_94)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_93)) :args ((or _let_54 _let_93 (not _let_92)))) _let_78 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_96)) :args ((or _let_1 _let_55 _let_54 _let_92 (not _let_96)))) _let_89 _let_71 _let_78 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_98 :args (tptp.xm tptp.xn QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_97))) _let_98 :args (_let_96 false _let_97)) :args (_let_92 true _let_1 false _let_15 false _let_14 false _let_96)) :args (_let_93 false _let_14 false _let_92)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_74 :args _let_95) :args _let_73)) _let_72 :args (_let_94 false _let_11)) :args (_let_26 false _let_93 false _let_94)) :args (_let_90 true _let_25 false _let_26)) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM2 (ALPHA_EQUIV :args (_let_24 (= W0 W0)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_30 4)) :args ((or _let_29 (not _let_30)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_IMPLIES_NEG1 :args _let_58) :args ((or _let_30 _let_31))) (MACRO_RESOLUTION_TRUST _let_59 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_IMPLIES_NEG1 :args _let_60) :args ((or _let_1 _let_35))) _let_89 :args (_let_35 true _let_1)) :args ((not _let_31) false _let_35)) :args (_let_30 true _let_31)) :args (_let_29 false _let_30)) :args (_let_24 false _let_29)) :args (false true _let_28 false _let_24)) :args ((forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) true)) (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) true)) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElement0 W1))))) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (=> (tptp.isFinite0 W0) true))) (forall ((W0 $$unsorted)) (= (= W0 tptp.slcrc0) (and (tptp.aSet0 W0) (not (exists ((W1 $$unsorted)) (tptp.aElementOf0 W1 W0)))))) (tptp.isFinite0 tptp.slcrc0) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (=> (tptp.isCountable0 W0) true))) (forall ((W0 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.isCountable0 W0)) (not (tptp.isFinite0 W0)))) (forall ((W0 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.isCountable0 W0)) (not (= W0 tptp.slcrc0)))) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (= (tptp.aSubsetOf0 W1 W0) (and (tptp.aSet0 W1) (forall ((W2 $$unsorted)) (=> (tptp.aElementOf0 W2 W1) (tptp.aElementOf0 W2 W0)))))))) (forall ((W0 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.isFinite0 W0)) (forall ((W1 $$unsorted)) (=> (tptp.aSubsetOf0 W1 W0) (tptp.isFinite0 W1))))) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (tptp.aSubsetOf0 W0 W0))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.aSet0 W1)) (=> (and (tptp.aSubsetOf0 W0 W1) (tptp.aSubsetOf0 W1 W0)) (= W0 W1)))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.aSet0 W1) (tptp.aSet0 W2)) (=> (and (tptp.aSubsetOf0 W0 W1) (tptp.aSubsetOf0 W1 W2)) (tptp.aSubsetOf0 W0 W2)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.aElement0 W1)) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtpldt0 W0 W1)) (and (tptp.aSet0 W2) (forall ((W3 $$unsorted)) (= (tptp.aElementOf0 W3 W2) (and (tptp.aElement0 W3) (or (tptp.aElementOf0 W3 W0) (= W3 W1)))))))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.aElement0 W1)) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtmndt0 W0 W1)) (and (tptp.aSet0 W2) (forall ((W3 $$unsorted)) (= (tptp.aElementOf0 W3 W2) (and (tptp.aElement0 W3) (tptp.aElementOf0 W3 W0) (not (= W3 W1)))))))))) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (= (tptp.sdtpldt0 (tptp.sdtmndt0 W0 W1) W1) W0))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aSet0 W1)) (=> (not (tptp.aElementOf0 W0 W1)) (= (tptp.sdtmndt0 (tptp.sdtpldt0 W1 W0) W0) W1)))) (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (forall ((W1 $$unsorted)) (=> (and (tptp.aSet0 W1) (tptp.isCountable0 W1)) (tptp.isCountable0 (tptp.sdtpldt0 W1 W0)))))) (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (forall ((W1 $$unsorted)) (=> (and (tptp.aSet0 W1) (tptp.isCountable0 W1)) (tptp.isCountable0 (tptp.sdtmndt0 W1 W0)))))) (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (forall ((W1 $$unsorted)) (=> (and (tptp.aSet0 W1) (tptp.isFinite0 W1)) (tptp.isFinite0 (tptp.sdtpldt0 W1 W0)))))) (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (forall ((W1 $$unsorted)) (=> (and (tptp.aSet0 W1) (tptp.isFinite0 W1)) (tptp.isFinite0 (tptp.sdtmndt0 W1 W0)))))) (and (tptp.aSet0 tptp.szNzAzT0) (tptp.isCountable0 tptp.szNzAzT0)) (tptp.aElementOf0 tptp.sz00 tptp.szNzAzT0) _let_23 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (=> (= (tptp.szszuzczcdt0 W0) (tptp.szszuzczcdt0 W1)) (= W0 W1)))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (or (= W0 tptp.sz00) (exists ((W1 $$unsorted)) (and (tptp.aElementOf0 W1 tptp.szNzAzT0) (= W0 (tptp.szszuzczcdt0 W1))))))) _let_22 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (=> (tptp.sdtlseqdt0 W0 W1) true))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.sdtlseqdt0 tptp.sz00 W0))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (not (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 W0) tptp.sz00)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (= (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 (tptp.szszuzczcdt0 W0) (tptp.szszuzczcdt0 W1))))) _let_21 (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.sdtlseqdt0 W0 W0))) _let_20 _let_19 _let_18 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (=> (tptp.iLess0 W0 W1) true))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.iLess0 W0 (tptp.szszuzczcdt0 W0)))) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (tptp.aElement0 (tptp.sbrdtbr0 W0)))) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (= (tptp.aElementOf0 (tptp.sbrdtbr0 W0) tptp.szNzAzT0) (tptp.isFinite0 W0)))) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (= (= (tptp.sbrdtbr0 W0) tptp.sz00) (= W0 tptp.slcrc0)))) (forall ((W0 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.isFinite0 W0)) (forall ((W1 $$unsorted)) (=> (tptp.aElement0 W1) (=> (not (tptp.aElementOf0 W1 W0)) (= (tptp.sbrdtbr0 (tptp.sdtpldt0 W0 W1)) (tptp.szszuzczcdt0 (tptp.sbrdtbr0 W0)))))))) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (and (tptp.isFinite0 W0) (tptp.aElementOf0 W1 W0)) (= (tptp.szszuzczcdt0 (tptp.sbrdtbr0 (tptp.sdtmndt0 W0 W1))) (tptp.sbrdtbr0 W0)))))) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (and (tptp.isFinite0 W0) (tptp.aSubsetOf0 W1 W0)) (tptp.sdtlseqdt0 (tptp.sbrdtbr0 W1) (tptp.sbrdtbr0 W0)))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (=> (and (tptp.isFinite0 W0) (tptp.sdtlseqdt0 W1 (tptp.sbrdtbr0 W0))) (exists ((W2 $$unsorted)) (and (tptp.aSubsetOf0 W2 W0) (= (tptp.sbrdtbr0 W2) W1)))))) (forall ((W0 $$unsorted)) (=> (and (tptp.aSubsetOf0 W0 tptp.szNzAzT0) (not (= W0 tptp.slcrc0))) (forall ((W1 $$unsorted)) (= (= W1 (tptp.szmzizndt0 W0)) (and (tptp.aElementOf0 W1 W0) (forall ((W2 $$unsorted)) (=> (tptp.aElementOf0 W2 W0) (tptp.sdtlseqdt0 W1 W2)))))))) (forall ((W0 $$unsorted)) (=> (and (tptp.aSubsetOf0 W0 tptp.szNzAzT0) (tptp.isFinite0 W0) (not (= W0 tptp.slcrc0))) (forall ((W1 $$unsorted)) (= (= W1 (tptp.szmzazxdt0 W0)) (and (tptp.aElementOf0 W1 W0) (forall ((W2 $$unsorted)) (=> (tptp.aElementOf0 W2 W0) (tptp.sdtlseqdt0 W2 W1)))))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (let ((_let_1 (tptp.szmzizndt0 W1))) (let ((_let_2 (tptp.szmzizndt0 W0))) (=> (and (tptp.aSubsetOf0 W0 tptp.szNzAzT0) (tptp.aSubsetOf0 W1 tptp.szNzAzT0) (not (= W0 tptp.slcrc0)) (not (= W1 tptp.slcrc0))) (=> (and (tptp.aElementOf0 _let_2 W1) (tptp.aElementOf0 _let_1 W0)) (= _let_2 _let_1)))))) _let_17 (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.isFinite0 (tptp.slbdtrb0 W0)))) (= (tptp.slbdtrb0 tptp.sz00) tptp.slcrc0) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.szNzAzT0) (tptp.aElementOf0 W1 tptp.szNzAzT0)) (= (tptp.aElementOf0 W0 (tptp.slbdtrb0 (tptp.szszuzczcdt0 W1))) (or (tptp.aElementOf0 W0 (tptp.slbdtrb0 W1)) (= W0 W1))))) _let_16 _let_13 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 10.53/11.04 )
% 10.53/11.04 % SZS output end Proof for NUM542+2
% 10.53/11.04 % cvc5---1.0.5 exiting
% 10.53/11.04 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------